Analysis¶

In [ ]:
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import sklearn as sk
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
import statsmodels.formula.api as smf
from bokeh.plotting import figure, output_file, show
from bokeh.palettes import magma
from plotnine import ggplot, aes, geom_point, theme_minimal, labs, theme, element_blank
from sklearn.experimental import enable_iterative_imputer
from sklearn.impute import IterativeImputer
import statsmodels.stats.diagnostic as ssd
import  statsmodels.stats.outliers_influence as oi
import statsmodels.stats.anova as av
import statsmodels.stats.oneway as ow
from statsmodels.tsa.stattools import adfuller
from scipy.stats import f_oneway
from statsmodels.stats.multicomp import pairwise_tukeyhsd

Read File

In [ ]:
bab = pd.read_csv("cleanning.ipynb (cbab).csv")
In [ ]:
ba1=np.log(bab[["bwt","gestation","age","height","weight"]])
In [ ]:
ba2=bab[["parity","smoke"]]
In [ ]:
bab=pd.concat([ba1,ba2],axis=1)
In [ ]:
bab.head()
Out[ ]:
bwt gestation age height weight parity smoke
0 4.787492 5.648974 3.295837 4.127134 4.605170 0 0
1 4.727388 5.641907 3.496508 4.158883 4.905275 0 0
2 4.852030 5.631212 3.332205 4.158883 4.744932 0 1
3 4.812184 5.622575 3.583519 4.234107 5.247024 0 0
4 4.682131 5.641907 3.135494 4.204693 4.828314 0 1

Explore Data

In [ ]:
bab.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1236 entries, 0 to 1235
Data columns (total 7 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   bwt        1236 non-null   float64
 1   gestation  1236 non-null   float64
 2   age        1236 non-null   float64
 3   height     1236 non-null   float64
 4   weight     1236 non-null   float64
 5   parity     1236 non-null   int64  
 6   smoke      1236 non-null   int64  
dtypes: float64(5), int64(2)
memory usage: 67.7 KB
In [ ]:
bab.describe()
Out[ ]:
bwt gestation age height weight parity smoke
count 1236.000000 1236.000000 1236.000000 1236.000000 1236.000000 1236.000000 1236.000000
mean 4.771633 5.630639 3.283400 4.158885 4.844823 0.254854 0.391586
std 0.160172 0.059443 0.207776 0.039359 0.151909 0.435956 0.488302
min 4.007333 4.997212 2.708050 3.970292 4.465908 0.000000 0.000000
25% 4.689044 5.605802 3.135494 4.127134 4.744932 0.000000 0.000000
50% 4.787492 5.634790 3.258097 4.158883 4.828314 0.000000 0.000000
75% 4.875197 5.662960 3.433987 4.189655 4.927254 1.000000 1.000000
max 5.170484 5.866468 3.806662 4.276666 5.521461 1.000000 1.000000

change type for column smoke

In [ ]:
bab['smoke'].astype('int')
Out[ ]:
0       0
1       0
2       1
3       0
4       1
       ..
1231    0
1232    0
1233    1
1234    0
1235    0
Name: smoke, Length: 1236, dtype: int32
In [ ]:
bab.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1236 entries, 0 to 1235
Data columns (total 7 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   bwt        1236 non-null   float64
 1   gestation  1236 non-null   float64
 2   age        1236 non-null   float64
 3   height     1236 non-null   float64
 4   weight     1236 non-null   float64
 5   parity     1236 non-null   int64  
 6   smoke      1236 non-null   int64  
dtypes: float64(5), int64(2)
memory usage: 67.7 KB

multicollinearity test if more than 10 so there multicollinearity, if less than 10 so there non multicollinearity

In [ ]:
x=bab[['bwt', 'gestation', 'parity', 'age', 'height', 'weight','smoke']]
In [ ]:
vif = [oi.variance_inflation_factor(x.values, i) for i in range(len(x.columns))]
vif
Out[ ]:
[1157.8078523648064,
 6459.0755962720605,
 1.573709336525281,
 291.48202863320165,
 7457.291403567023,
 1338.0145200029037,
 1.7717211734026819]

**Exploratry Analysis **¶

Heatmap to see correlation DarkRed is perfect positive correlation blue is negitive perfect correlation

In [ ]:
sns.set_theme()
sns.set_palette("coolwarm") 

plt.figure(figsize=(30, 16))
heatmap = sns.heatmap(bab.corr(), annot=True, cmap="coolwarm", fmt=".2f", linewidths=0.5, vmin=-1, vmax=1)


for text in heatmap.texts:
    text.set_size(10)


plt.title("Correlation Heatmap of bab DataFrame", fontsize=20)


plt.tight_layout()


plt.show()
No description has been provided for this image

pie chart

In [ ]:
plt.figure(figsize=(7,5))
colors = ['#66b3ff', '#99ff99']  
explode = (0.1, 0)  
ax = bab.value_counts('smoke').plot(kind='pie', autopct='%1.0f%%', startangle=90,colors=colors, explode=explode, shadow=True)
ax.set_title('Distribution of Smoke')
ax.set_ylabel('')
ax.legend(labels=bab['smoke'].value_counts().index, loc='upper right')
ax.axis('equal')
plt.show()
No description has been provided for this image
In [ ]:
plt.figure(figsize=(7,5))
colors = ['#66b3ff', '#99ff99']  
explode = (0.1, 0)  
ax = bab.value_counts('parity').plot(kind='pie', autopct='%1.0f%%', startangle=90,colors=colors, explode=explode, shadow=True)
ax.set_title('Distribution of parity')
ax.set_ylabel('')
ax.legend(labels=bab['parity'].value_counts().index, loc='upper right')
ax.axis('equal')
plt.show()
No description has been provided for this image

scatter matrix to see realtion between two varaible

In [ ]:
pd.plotting.scatter_matrix(bab,figsize=(20,15),diagonal="hist")
plt.show()
No description has been provided for this image

BoxPlot

In [ ]:
fig, axes = plt.subplots(nrows=len(bab.columns), figsize=(15, 20), sharex=False)


sns.set(style="whitegrid")

# Define a color palette for the box plots
custom_palette = sns.color_palette("husl")

for i, column in enumerate(bab.columns):
    sns.boxplot(x=bab[column], ax=axes[i], color=custom_palette[i % len(custom_palette)])
    axes[i].set_title(column, fontsize=16)
    axes[i].tick_params(labelsize=12)

# Adjust layout for better spacing
plt.tight_layout()

plt.suptitle("Box Plots of Numeric Variables", y=0.92, fontsize=20)
plt.show()
No description has been provided for this image

Histogram for each varible

In [ ]:
sns.set_theme()
sns.set_palette("pastel")  

fig, axes = plt.subplots(nrows=4, ncols=2, figsize=(20, 20))

# Flatten the axes array for easier iteration
axes = axes.flatten()

# Loop through columns and create histograms
for i, column in enumerate(bab.columns):
    sns.histplot(bab[column], ax=axes[i], kde=True, color='green', bins=20)
    axes[i].set_title(column, fontsize=14)
    axes[i].set_xlabel(column, fontsize=12)

# Adjust layout
plt.tight_layout()

# Show the plot
plt.show()
No description has been provided for this image

multipyle linear regression¶

**H0 : (no linear relationship between depnedant variabels and indepnedant)

H1 : (linear relationship between depnedant variabels and indepnedant)

alpha = 0.05**

In [ ]:
bab_model = smf.ols('(bwt) ~ age + gestation + weight + height',data =bab).fit()
bab_model.summary()
Out[ ]:
OLS Regression Results
Dep. Variable: bwt R-squared: 0.217
Model: OLS Adj. R-squared: 0.214
Method: Least Squares F-statistic: 85.25
Date: Sat, 30 Dec 2023 Prob (F-statistic): 5.86e-64
Time: 19:40:12 Log-Likelihood: 661.54
No. Observations: 1236 AIC: -1313.
Df Residuals: 1231 BIC: -1287.
Df Model: 4
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept -4.2103 0.571 -7.372 0.000 -5.331 -3.090
age 0.0254 0.020 1.283 0.200 -0.013 0.064
gestation 1.1345 0.068 16.641 0.000 1.001 1.268
weight 0.0876 0.031 2.861 0.004 0.028 0.148
height 0.5017 0.117 4.294 0.000 0.272 0.731
Omnibus: 55.861 Durbin-Watson: 2.030
Prob(Omnibus): 0.000 Jarque-Bera (JB): 86.005
Skew: -0.386 Prob(JB): 2.11e-19
Kurtosis: 4.037 Cond. No. 1.32e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.32e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

all reject H0 ,age accept H0

**Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)

Alternative Hypothesis (HA): Heteroscedasticity is present (the residuals are not distributed with equal variance)

rejectH0**

In [ ]:
bmb_hetro = ssd.het_breuschpagan(bab_model.resid,bab_model.model.exog)
bmb_hetro_test_statistic, bmb_hetro_p_value = bmb_hetro[:2]
bmb_hetro_test_statistic, bmb_hetro_p_value
Out[ ]:
(107.18832188232055, 2.893995401616934e-22)

weighted least square bab_model_weight¶

In [ ]:
waight =1/(bab_model.resid**2)
bab_model_weight = smf.wls('(bwt) ~ age + gestation + weight + height',data=bab,weights=waight).fit()
bab_model_weight.summary()
Out[ ]:
WLS Regression Results
Dep. Variable: bwt R-squared: 0.999
Model: WLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 3.978e+05
Date: Sat, 30 Dec 2023 Prob (F-statistic): 0.00
Time: 19:40:12 Log-Likelihood: 1531.0
No. Observations: 1236 AIC: -3052.
Df Residuals: 1231 BIC: -3026.
Df Model: 4
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept -4.2268 0.019 -220.232 0.000 -4.264 -4.189
age 0.0252 0.001 20.168 0.000 0.023 0.028
gestation 1.1348 0.002 666.563 0.000 1.131 1.138
weight 0.0861 0.002 48.370 0.000 0.083 0.090
height 0.5071 0.006 88.545 0.000 0.496 0.518
Omnibus: 4668.638 Durbin-Watson: 2.056
Prob(Omnibus): 0.000 Jarque-Bera (JB): 204.910
Skew: -0.171 Prob(JB): 3.19e-45
Kurtosis: 1.035 Cond. No. 3.03e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.03e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

All Reject H0

**Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)

Alternative Hypothesis (HA): Heteroscedasticity is present (the residuals are not distributed with equal variance)

rejectH0**

In [ ]:
bmbww_hetro = ssd.het_breuschpagan(bab_model_weight.resid,bab_model_weight.model.exog)
bmbww_hetro_test_statistic, bmbww_hetro_p_value = bmbww_hetro[:2]
bmbww_hetro_test_statistic, bmbww_hetro_p_value
Out[ ]:
(107.23976957030139, 2.82182903132245e-22)

to show assumption

In [ ]:
residuals = bab_model_weight.resid
fitted = bab_model_weight.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()
No description has been provided for this image
In [ ]:
bab.columns
Out[ ]:
Index(['bwt', 'gestation', 'age', 'height', 'weight', 'parity', 'smoke'], dtype='object')

remove outlier

In [ ]:
quantiles = bab.quantile([0.1, 0.9])
low = quantiles.loc[0.1]
high = quantiles.loc[0.9]

df = bab[(bab >= low) & (bab <= high)]
In [ ]:
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1236 entries, 0 to 1235
Data columns (total 7 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   bwt        998 non-null    float64
 1   gestation  997 non-null    float64
 2   age        1052 non-null   float64
 3   height     1047 non-null   float64
 4   weight     1004 non-null   float64
 5   parity     1236 non-null   int64  
 6   smoke      1236 non-null   int64  
dtypes: float64(5), int64(2)
memory usage: 67.7 KB
In [ ]:
bab.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1236 entries, 0 to 1235
Data columns (total 7 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   bwt        1236 non-null   float64
 1   gestation  1236 non-null   float64
 2   age        1236 non-null   float64
 3   height     1236 non-null   float64
 4   weight     1236 non-null   float64
 5   parity     1236 non-null   int64  
 6   smoke      1236 non-null   int64  
dtypes: float64(5), int64(2)
memory usage: 67.7 KB

we make multiple imputaion for variable that have missing

In [ ]:
imputer = IterativeImputer()
fit_imput = imputer.fit_transform(df)
cdf = pd.DataFrame(fit_imput, columns = df.columns)

BoxPlot after Outlier and impute

In [ ]:
fig, axes = plt.subplots(nrows=len(cdf.columns), figsize=(15, 20), sharex=False)


sns.set(style="whitegrid")

# Define a color palette for the box plots
custom_palette = sns.color_palette("husl")

for i, column in enumerate(bab.columns):
    sns.boxplot(x=cdf[column], ax=axes[i], color=custom_palette[i % len(custom_palette)])
    axes[i].set_title(column, fontsize=16)
    axes[i].tick_params(labelsize=12)

# Adjust layout for better spacing
plt.tight_layout()

plt.suptitle("Box Plots of Numeric Variables", y=0.92, fontsize=20)
plt.show()
No description has been provided for this image
In [ ]:
cdf.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1236 entries, 0 to 1235
Data columns (total 7 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   bwt        1236 non-null   float64
 1   gestation  1236 non-null   float64
 2   age        1236 non-null   float64
 3   height     1236 non-null   float64
 4   weight     1236 non-null   float64
 5   parity     1236 non-null   float64
 6   smoke      1236 non-null   float64
dtypes: float64(7)
memory usage: 67.7 KB

we make cbab_model after outlier

In [ ]:
cbab_model = smf.ols('(bwt) ~ age + gestation + weight + height',data =cdf).fit()
cbab_model.summary()
Out[ ]:
OLS Regression Results
Dep. Variable: bwt R-squared: 0.151
Model: OLS Adj. R-squared: 0.149
Method: Least Squares F-statistic: 54.93
Date: Sat, 30 Dec 2023 Prob (F-statistic): 1.19e-42
Time: 19:40:14 Log-Likelihood: 1321.2
No. Observations: 1236 AIC: -2632.
Df Residuals: 1231 BIC: -2607.
Df Model: 4
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept -3.9218 0.616 -6.362 0.000 -5.131 -2.712
age 0.0233 0.016 1.455 0.146 -0.008 0.055
gestation 1.1086 0.091 12.176 0.000 0.930 1.287
weight 0.1058 0.029 3.599 0.000 0.048 0.163
height 0.4491 0.099 4.529 0.000 0.255 0.644
Omnibus: 10.924 Durbin-Watson: 1.987
Prob(Omnibus): 0.004 Jarque-Bera (JB): 11.134
Skew: -0.226 Prob(JB): 0.00382
Kurtosis: 2.893 Cond. No. 2.41e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.41e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

all reject H0 except age accept H0

**Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)

Alternative Hypothesis (HA): Heteroscedasticity is present (the residuals are not distributed with equal variance)

rejectH0**

In [ ]:
bibaf_hetro = ssd.het_breuschpagan(cbab_model.resid,cbab_model.model.exog)
bibaf_hetro_test_statistic, bibaf_hetro_p_value = bibaf_hetro[:2]
bibaf_hetro_test_statistic, bibaf_hetro_p_value
Out[ ]:
(5.70649144103303, 0.22216612123537832)
In [ ]:
residuals = cbab_model.resid
fitted = cbab_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()
No description has been provided for this image

Weight least square after outlier

In [ ]:
waight =1/(cbab_model.resid**2)
cdf_model_weight = smf.wls('(bwt) ~ age + gestation + weight + height',data=cdf,weights=waight).fit()
cdf_model_weight.summary()
Out[ ]:
WLS Regression Results
Dep. Variable: bwt R-squared: 0.988
Model: WLS Adj. R-squared: 0.988
Method: Least Squares F-statistic: 2.591e+04
Date: Sat, 30 Dec 2023 Prob (F-statistic): 0.00
Time: 19:40:15 Log-Likelihood: 2193.3
No. Observations: 1236 AIC: -4377.
Df Residuals: 1231 BIC: -4351.
Df Model: 4
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept -3.9653 0.033 -120.530 0.000 -4.030 -3.901
age 0.0260 0.001 19.837 0.000 0.023 0.029
gestation 1.1126 0.006 174.798 0.000 1.100 1.125
weight 0.1064 0.001 74.315 0.000 0.104 0.109
height 0.4513 0.004 103.787 0.000 0.443 0.460
Omnibus: 4633.076 Durbin-Watson: 1.998
Prob(Omnibus): 0.000 Jarque-Bera (JB): 203.273
Skew: -0.102 Prob(JB): 7.24e-45
Kurtosis: 1.024 Cond. No. 3.33e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.33e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

all rejectH0

**Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)

Alternative Hypothesis (HA): Heteroscedasticity is present (the residuals are not distributed with equal variance)

Reject H0**

In [ ]:
bibwwaf_hetro = ssd.het_breuschpagan(cdf_model_weight.resid,cdf_model_weight.model.exog)
bibwwaf_hetro_test_statistic, bibwwaf_hetro_p_value = bibwwaf_hetro[:2]
bibwwaf_hetro_test_statistic, bibwwaf_hetro_p_value
Out[ ]:
(5.73702670622447, 0.219666879038615)
In [ ]:
residuals = cdf_model_weight.resid
fitted = cdf_model_weight.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()
No description has been provided for this image

test without Age

In [ ]:
waight =1/(cbab_model.resid**2)
cdf_model_weight_withoutage = smf.wls('(bwt) ~ gestation + weight + height',data=cdf,weights=waight).fit()
cdf_model_weight_withoutage.summary()
Out[ ]:
WLS Regression Results
Dep. Variable: bwt R-squared: 0.985
Model: WLS Adj. R-squared: 0.984
Method: Least Squares F-statistic: 2.610e+04
Date: Sat, 30 Dec 2023 Prob (F-statistic): 0.00
Time: 19:40:15 Log-Likelihood: 2021.9
No. Observations: 1236 AIC: -4036.
Df Residuals: 1232 BIC: -4015.
Df Model: 3
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept -3.6506 0.033 -110.305 0.000 -3.716 -3.586
gestation 1.0654 0.007 157.184 0.000 1.052 1.079
weight 0.0934 0.001 63.879 0.000 0.091 0.096
height 0.4750 0.005 98.937 0.000 0.466 0.484
Omnibus: 42.391 Durbin-Watson: 1.992
Prob(Omnibus): 0.000 Jarque-Bera (JB): 109.935
Skew: 0.053 Prob(JB): 1.34e-24
Kurtosis: 4.457 Cond. No. 2.74e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.74e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

all reject

**Null Hypothesis (H0): Homoscedasticity is present (the residuals are distributed with equal variance)

Alternative Hypothesis (HA): Heteroscedasticity is present (the residuals are not distributed with equal variance)

Reject H0**

In [ ]:
bibwwage_hetro = ssd.het_breuschpagan(cdf_model_weight_withoutage.resid,cdf_model_weight_withoutage.model.exog)
bibwwage_hetro_test_statistic, bibwwage_hetro_p_value = bibwwage_hetro[:2]
bibwwage_hetro_test_statistic, bibwwage_hetro_p_value
Out[ ]:
(5.210367761272021, 0.15702537815839604)
In [ ]:
residuals = cdf_model_weight_withoutage.resid
fitted = cdf_model_weight_withoutage.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()
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all reject except age accept H0

scatter matrix after outlier

In [ ]:
pd.plotting.scatter_matrix(cdf,figsize=(20,20),diagonal="hist")
plt.show()
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line chart for each variable

In [ ]:
for column in df.columns:
    plt.figure(figsize=(20,5))
    plt.plot(df.index, df[column], label=column)
    plt.xlabel('Index')
    plt.ylabel('Values')
    plt.title('Line Charts for DataFrame Columns')
    plt.legend()
    plt.show()
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stationarity test

In [ ]:
for i in cdf.columns:
    test =adfuller(cdf[i])
    print(test[0:2])

(-34.9014565897187, 0.0)
(-21.412343969762823, 0.0)
(-17.621118681748897, 3.838193005054726e-30)
(-25.083894900428195, 0.0)
(-24.79702513755696, 0.0)
(-5.401475040840921, 3.36312456935009e-06)
(-36.288736504291386, 0.0)

logistic reggression¶

In [ ]:
bab_model2 = smf.logit('(parity)~ (age)+(weight)',data=cdf).fit()
bab_model2.summary()

Optimization terminated successfully.
         Current function value: 0.516681
         Iterations 6
Out[ ]:
Logit Regression Results
Dep. Variable: parity No. Observations: 1236
Model: Logit Df Residuals: 1233
Method: MLE Df Model: 2
Date: Sat, 30 Dec 2023 Pseudo R-squ.: 0.08972
Time: 19:40:21 Log-Likelihood: -638.62
converged: True LL-Null: -701.56
Covariance Type: nonrobust LLR p-value: 4.614e-28
coef std err z P>|z| [0.025 0.975]
Intercept 21.3247 3.981 5.356 0.000 13.521 29.128
age -5.2441 0.519 -10.101 0.000 -6.262 -4.226
weight -1.1162 0.780 -1.431 0.152 -2.645 0.413
In [ ]:
parity_model = smf.logit("parity ~ gestation", data = cdf).fit()
parity_model.summary()

Optimization terminated successfully.
         Current function value: 0.563829
         Iterations 6
Out[ ]:
Logit Regression Results
Dep. Variable: parity No. Observations: 1236
Model: Logit Df Residuals: 1234
Method: MLE Df Model: 1
Date: Sat, 30 Dec 2023 Pseudo R-squ.: 0.006653
Time: 19:40:21 Log-Likelihood: -696.89
converged: True LL-Null: -701.56
Covariance Type: nonrobust LLR p-value: 0.002248
coef std err z P>|z| [0.025 0.975]
Intercept -44.5681 14.350 -3.106 0.002 -72.693 -16.443
gestation 7.7193 2.546 3.032 0.002 2.729 12.710

Anova¶

In [ ]:
smoke_modlano = smf.ols("bwt ~ smoke", data = cdf).fit()
smoke_modlano.summary()
Out[ ]:
OLS Regression Results
Dep. Variable: bwt R-squared: 0.065
Model: OLS Adj. R-squared: 0.064
Method: Least Squares F-statistic: 85.08
Date: Sat, 30 Dec 2023 Prob (F-statistic): 1.20e-19
Time: 19:40:21 Log-Likelihood: 1261.0
No. Observations: 1236 AIC: -2518.
Df Residuals: 1234 BIC: -2508.
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept 4.7980 0.003 1507.024 0.000 4.792 4.804
smoke -0.0469 0.005 -9.224 0.000 -0.057 -0.037
Omnibus: 22.937 Durbin-Watson: 1.991
Prob(Omnibus): 0.000 Jarque-Bera (JB): 20.287
Skew: -0.256 Prob(JB): 3.93e-05
Kurtosis: 2.638 Cond. No. 2.44


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
In [ ]:
av.anova_lm(smoke_modlano)
Out[ ]:
df sum_sq mean_sq F PR(>F)
smoke 1.0 0.648545 0.648545 85.082092 1.202803e-19
Residual 1234.0 9.406260 0.007623 NaN NaN
In [ ]:
bwt_anova = smf.ols("bwt ~ smoke +weight" , data = cdf).fit()
In [ ]:
bwt_anova.summary()
Out[ ]:
OLS Regression Results
Dep. Variable: bwt R-squared: 0.090
Model: OLS Adj. R-squared: 0.089
Method: Least Squares F-statistic: 60.96
Date: Sat, 30 Dec 2023 Prob (F-statistic): 5.69e-26
Time: 19:40:21 Log-Likelihood: 1278.0
No. Observations: 1236 AIC: -2550.
Df Residuals: 1233 BIC: -2535.
Df Model: 2
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept 4.0150 0.133 30.121 0.000 3.754 4.277
smoke -0.0459 0.005 -9.143 0.000 -0.056 -0.036
weight 0.1618 0.028 5.876 0.000 0.108 0.216
Omnibus: 16.259 Durbin-Watson: 2.019
Prob(Omnibus): 0.000 Jarque-Bera (JB): 15.473
Skew: -0.237 Prob(JB): 0.000437
Kurtosis: 2.726 Cond. No. 275.


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
In [ ]:
av.anova_lm(bwt_anova)
Out[ ]:
df sum_sq mean_sq F PR(>F)
smoke 1.0 0.648545 0.648545 87.393382 4.039092e-20
weight 1.0 0.256188 0.256188 34.522131 5.415991e-09
Residual 1233.0 9.150071 0.007421 NaN NaN
In [ ]:
bwt_anova = smf.ols("bwt ~ smoke +weight+smoke:weight" , data = cdf).fit()
In [ ]:
av.anova_lm(bwt_anova)
Out[ ]:
df sum_sq mean_sq F PR(>F)
smoke 1.0 0.648545 0.648545 87.424518 3.984831e-20
weight 1.0 0.256188 0.256188 34.534430 5.383883e-09
smoke:weight 1.0 0.010677 0.010677 1.439274 2.304875e-01
Residual 1232.0 9.139394 0.007418 NaN NaN
In [ ]:
from statsmodels.stats.multicomp import pairwise_tukeyhsd
tukey = pairwise_tukeyhsd(endog=cdf['bwt'],groups=cdf['smoke'],alpha=0.05)
print(tukey)

Multiple Comparison of Means - Tukey HSD, FWER=0.05
===================================================
group1 group2 meandiff p-adj  lower   upper  reject
---------------------------------------------------
   0.0    1.0  -0.0469   0.0 -0.0569 -0.0369   True
---------------------------------------------------
In [ ]:
for i in cdf.columns:
    test =adfuller(cdf[i])
    print(test[0:2])

(-34.9014565897187, 0.0)
(-21.412343969762823, 0.0)
(-17.621118681748897, 3.838193005054726e-30)
(-25.083894900428195, 0.0)
(-24.79702513755696, 0.0)
(-5.401475040840921, 3.36312456935009e-06)
(-36.288736504291386, 0.0)
In [ ]:
df_first_diff = cdf.diff()
In [ ]:
print(df_first_diff.isnull().sum())

bwt          1
gestation    1
age          1
height       1
weight       1
parity       1
smoke        1
dtype: int64
In [ ]:
df_first_diff=df_first_diff.dropna()
In [ ]:
print(df_first_diff.isnull().sum())

bwt          0
gestation    0
age          0
height       0
weight       0
parity       0
smoke        0
dtype: int64
In [ ]:
for i in df_first_diff.columns:
    test =adfuller(df_first_diff[i])
    print(test[0:2])

(-13.872822070606595, 6.418146448168798e-26)
(-12.599449904649616, 1.7492435803149162e-23)
(-13.141361943053036, 1.4271732490729154e-24)
(-12.2345595320091, 1.0352138449527491e-22)
(-15.925884769769677, 7.828485404189162e-29)
(-14.143680218295682, 2.2232953489488007e-26)
(-14.7880975162883, 2.192598720103753e-27)
In [ ]:
df_second_diff = df_first_diff.diff()
In [ ]:
df_second_diff=df_second_diff.dropna()
In [ ]:
for i in df_second_diff.columns:
    test =adfuller(df_second_diff[i])
    print(test[0:2])

(-16.6499138487741, 1.6073778437894496e-29)
(-15.43382373474774, 2.9247883405264146e-28)
(-16.377134430341457, 2.774144700333838e-29)
(-15.278548914909132, 4.611734073186389e-28)
(-15.61124591190266, 1.7787046841662362e-28)
(-16.06023524002358, 5.649348055804563e-29)
(-16.453106522041107, 2.368200398722271e-29)